Question

Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 15 hours to drain the pool by itself, how pump to drain the pool on its own?

Answer 1

The other pump would take 10 hours to drain the pool on its own.

Step-by-step explanation:

To find out how long it would take for the older pump to drain the pool on its own, we can use the concept of work.

Let's assume that the pool's capacity is 'C'.

If the older pump can drain the pool in 15 hours, then the rate at which it can drain the pool is 1/15 of the pool's capacity per hour, or (C/15) per hour.

Working together, the two pumps can drain the pool in 6 hours. Therefore, the rate at which they can drain the pool together is 1/6 of the pool's capacity per hour, or (C/6) per hour.

Since we know that the older pump can drain the pool at a rate of (C/15) per hour and the two pumps together can drain the pool at a rate of (C/6) per hour, we can subtract the rate of the older pump from the rate of the two pumps together to find the rate of the other pump:

(C/6) - (C/15) = (C/10) per hour.

Therefore, it would take the other pump 10 hours to drain the pool on its own.

Answer 2

10

Step-by-step explanation:

Rate of drainage for pump A and B = [1 pool drained]/[6 hours]

Rate of drainage for pump A (older pump) = [1 pool drained]/[15 hours]

Rate for pump B (newer pump) = [1 pool drained]/[t hours]

Thus, adding the rate of drainage of A and B,

1/t + 1/15 = 1/6

t=10